Derrick Bird, the gunman who killed 12 people in Cumbria, feared he would go to prison because of a tax investigation, it was reported today, as the prime minister arrived in Whitehaven to meet some of the injured.

David Cameron, accompanied by the home secretary, Theresa May, travelled first to West Cumberland hospital in Whitehaven, where five injured victims are being treated. The prime minister also talked to NHS staff who treated the first victims.

After his visit, Cameron said: "People – I have met some of them – are having to come to terms with the most appalling random acts that they will find very difficult to understand and in some cases there will be no proper explanation.

"But I do think it is important to thank the emergency services and the police for all they have done and to recognise that. As people's sadness and mourning will give way to a sense of numbness, then there will be lots of questions that people want to ask.

"We have to make sure that we find the right way to answer those questions and help this community through what is to be a very, very difficult time."

Earlier it was announced that one minute's silence would be held next Wednesday in the town and at five other places in Cumbria to remember Bird's victims.

Last night Bird's friend Mark Cooper revealed that HMRC was investigating Bird over a £60,000 sum deposited in his bank account. Cooper claimed that Bird was anxious about being sent to prison. "All he said was that they had caught him with £60,000 in the bank," he said.

Cooper, who had known Bird for 15 years, added: "He just asked me if he could handle jail. He didn't want to go." He said he was not sure where Bird had got the money but he claimed he was given £2,000 per month by his 90-year-old mother Mary.

A Cumbria police spokesman confirmed this morning that detectives were looking at the killer's finances and involvement with HMRC, saying: "It is an ongoing line of inquiry but there is no comment on that at this present moment."

Last night the daughters of Bird's twin brother, believed to be his first victim, denied there had been a family row over the mother's will.

In a statement, Rachel, 28, Tracey, 26, and Katie, 19, said: "We are utterly devastated about the death of our dad. He was the nicest man you could ever meet.

"He was a loving husband and doting dad and grandad. We would like to take this opportunity to say there was absolutely no family feud. Our dad's only downfall was to try to help his brother." David Bird, who lived alone, was found dead at his house in Lamplugh.

But speculation continues to focus on a possible family feud and a row Bird had with cab drivers in Whitehaven.

Witnesses said he had argued with drivers, including Darren Rewcastle, whom he shot at point blank range, over touting at the Duke Street rank in Whitehaven, where he worked.

Bird knew his first three victims. Police are investigating the possibility that some of the other nine may have been targeted by Bird or whether they were in the wrong place at the wrong time.

Most of those injured by Bird were shot in the face.

A Cumbria police spokesman said he could not "make any confirmations" of reports that Bird had self-harmed in the days before murdering 12 innocent people.

Asked when results of a postmortem would return, he said "a good few days".

Ryan Reed, assistant deputy coroner for west Cumbria, said there was no date yet to begin opening inquests.

Speaking to the Cumbria News & Star, Charles Brett, clinical director of emergency services at the West Cumberland hospital in Whitehaven, said: "It appears this gentleman was firing out of a car window at head height. It is clear that he was directing at the face and head."

He added: "More than 50% of those that survived had some portion of facial injuries."

The lead detective on the case, Chief Superintendent Ian Goulding, said police were looking at why certain individuals had been singled out. "A key part of the 'why' in this inquiry is to try to establish why those killed were chosen. Because of a … grudge or simply random killings," Goulding said.

"Our initial assessment shows we have a combination of both and I will not speculate further at this time."

Bird may have taken his motive to the grave, he added.

Police said that Bird had legally held the shotgun and the .22 rifle he used in the killings, but ministers ruled out what were described as "kneejerk curbs" on gun laws. Bird had held a shotgun licence for 15 years and a firearms licence covering the rifle since 2007. Police said he had never been to prison, although he was convicted of a theft offence 20 years ago. He had no history of mental health problems and there was no record of him being on medication.

Alan Johnson, the shadow home secretary, said there needed to be a review of the gun laws focusing on mental health checks on applicants for gun licences.

Seven of the 11 injured in the shooting spree remained in hospital yesterday. Two were in a serious but stable condition.

About 100 detectives are working on the case, described by Cumbria's chief constable, Craig Mackey, as "the most horrific incident I've seen in 25 years of policing". It also emerged that Bird was due to have an appointment with Kevin Commons, the family solicitor whom he killed, sometime on Wednesday, though it is unclear what it was about.

Iris Carruthers, 49, who went to secondary school with Bird, saw him in his taxi at the end of Commons's drive between 5.30 and 5.45am on Wednesday. She spoke to him, but he was "in a world of his own", she said.

As families of her son's victims tried to come to terms with Wednesday's nightmare, Bird's mother, who has cancer, cannot comprehend what has happened. Joy Ryan, a relative who lives in Rowrah, near the gunman's home, said: "I saw her yesterday and she was just stunned. She just couldn't make sense of it. She kept saying she wanted to talk to them, she wanted to talk to her sons," she told the Whitehaven News.